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A discontinuous Galerkin method for stochastic Cahn-Hilliard equations. (English) Zbl 1409.65073

Summary: In this paper, a discontinuous Galerkin method for the stochastic Cahn-Hilliard equation with additive random noise, which preserves the conservation of mass, is investigated. Numerical analysis and error estimates are carried out for the linearized stochastic Cahn-Hilliard equation. The effects of the noises on the accuracy of our scheme are also presented. Numerical examples simulated by Monte Carlo method for both linear and nonlinear stochastic Cahn-Hilliard equations are presented to illustrate the convergence rate and validate our conclusion.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
35R60 PDEs with randomness, stochastic partial differential equations
35K35 Initial-boundary value problems for higher-order parabolic equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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